In the Longest Increasing Subsequence (LIS) problem, "patience" refers to the ability to split and combine sequences of numbers. The algorithm involves finding the longest increasing subsequence in a given sequence.

DFS primarily employs Pre-order Traversal when traversing a graph. In Pre-order Traversal, the algorithm visits the root node, then recursively performs Pre-order Traversal on the left subtree and the right subtree.

The worst-case time complexity of the naive pattern matching algorithm is O(m * n), where 'm' is the length of the pattern and 'n' is the length of the text. This is because, in the worst case, the algorithm may need to compare each character of the pattern with each character of the text.

The time complexity of the dynamic programming approach for the longest common substring problem is O(nm), where 'n' and 'm' are the lengths of the input strings. The algorithm uses a table of size n x m to store intermediate results, leading to a quadratic time complexity.

Dijkstra's algorithm relies on the use of a priority queue to keep track of the shortest distances to each node efficiently. The priority queue ensures that nodes are processed in order of increasing distance, optimizing the exploration of the graph and helping in finding the shortest paths.

To efficiently represent a tic-tac-toe game board, a 2D array is commonly used. Each element of the array corresponds to a cell on the board, providing a straightforward and efficient way to simulate the grid.

The primary purpose of using a hash table is to achieve efficient data retrieval by mapping keys to values using a hash function. This allows for constant-time average-case complexity for basic operations like insertion, deletion, and search.

The space complexity of radix sort is O(1), indicating that it has a constant space requirement, making it more memory-efficient compared to other sorting algorithms like merge sort and quicksort.

Prim's algorithm typically performs better on graphs with sparse edges, where only a small number of edges exist. In contrast, Kruskal's algorithm is more efficient on graphs with dense edges, where a large number of edges are present. This is because the priority queue operations in Prim's algorithm are generally faster on sparse graphs.

In binary search, the array must be sorted to ensure correct results. Binary search relies on the property of a sorted array to efficiently eliminate half of the remaining elements in each step.

In certain applications like plagiarism detection, the longest common substring problem helps identify similarities between documents. By finding the longest common substring, one can detect shared sequences of words or characters, aiding in identifying potential instances of plagiarism.

The optimal substructure property in dynamic programming for the Knapsack Problem ensures that the solution to the overall problem can be constructed from optimal solutions to its overlapping subproblems, making it suitable for dynamic programming approaches.